1. Field of the Invention
The present invention relates to inductors for use in high frequency circuits, and more particularly to high frequency inductors integrated within semiconductor integrated circuitry.
2. Description of the Related Art
Efforts to fabricate large value inductors on silicon (Si) substrates for high frequency use during the 1960's proved ineffective. Self-resonance occurring within the inductive structure and low quality factors (Qs) limited inductor use at high frequencies. R. M. Warner, Ed., Integrated Circuits, Design Principles and Fabrication, McGraw Hill, 1965. Series resistance inherent within the aluminum/silicon formed inductors led to a reduction in quality factor with increasing frequency.
Typically, large value inductors are fabricated as aluminum (Al) or gold (Au) spirals with multiple turns on various semiconductor substrates. Increasing inductance, however, brings a concomitant increase in parasitic resistance (and capacitance), lowering the inductor's self-resonant frequency. For example, 25 nH spiral inductors fabricated with gold on GaAs or insulating sapphire substrates are found to self-resonate at approximately 3 GHz. In contrast, spiral inductors as small as 10 nH, formed with aluminum on Si substrates, are found to self-resonate at 2 GHz, and to display a decreased Q relative to the GaAs and insulated sapphire substrate formed inductors. Chang, et al., Large Suspended Inductors on Silicon And Their Use In A 2-.mu.m CMOS RF Amplifier, IEEE Electron Device Letters, Vol. 14, No. 5, pgs. 246-248, May, 1993.
Inductors formed by silicon process require relatively thin aluminum (A1) conductive layers (i.e., around 0.5 .mu.m), especially in multilevel designs, compared to the relatively thick gold (Au) conductive layers formed on column III-V semiconductors (i.e., around 6 .mu.m). The shallow depth of the A1 conductor lends itself to higher resistances relative to thicker conductive paths. The width (W) of an A1 layer disposed on a Si substrate may however, be increased to compensate for its shallow depth. The increased width results in an increased conductance and therefore an improvement in the inductor's Q. The relationship between the improved Q and increasing W, however, is not linear. At higher frequencies, current does not flow through the entire cross-sectional area of the conductor (i.e., all of the increased width), leading to current crowding. Improvement in Q with increasing conductive path width is found to diminish as W increases beyond 15 .mu.m, as shown in the plot of FIG. 1. Current crowding is believed to play a significant role in the changes in Q with increasing conductor width, becoming significant at widths beyond 15 .mu.m.
FIG. 2 shows a portion of a conventional spiral inductor L20 formed with an aluminum conductor 24 on a silicon substrate 22. W and L represent the conductor's width and length, respectively. Because the outer conductive path is longer than the inner conductive path, the effective resistance of the outer path is greater than that of the inner path. Current, therefore, taking the path of least resistance, tends to flow along the inner path, leading to current crowding. The current crowding effect appears to increase with increasing frequency. More specifically, the outer length, L.sub.o, of the conductor 24 is: ##EQU1## wherein N is the number within the spiral. The inner length, L.sub.i, is: ##EQU2## As L and/or W increases, L.sub.o /L.sub.i increases. At certain ratio or beyond, the current crowding occurs and the effective resistance increases which degrades the overall quality factor, Q.
For example, at N=1 and assuming W&gt;&gt;S, L.sub.o /L.sub.i =(4L-W)/(4L8W). If defining L.sub.o /L.sub.i &gt;1.5 as the threshold of significant current crowding, significant crowding should be found to occur at W&gt;L/5.5. Similarly at N=2, the defined threshold of current crowding occurs when W&gt;L/7; W&gt;L/8 in the case of N=3. With simple mathematics, the criterion for the threshold for current crowding at higher coil numbers can be easily derived. As N increases, the ratio of the outer length/inner length of tile inner conductor coils increases.